Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this map is a bijection and maps perturbed geodesics into perturbed Yang-Mills connections with the same Morse index.Comment: 58 pages, 3 figure

Hodge polynomials of some moduli spaces of Coherent Systems

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which $(n,d,k)=(3,d,1)$ and $d$ is even, obtaining from them the usual Poincar\'e polynomials.Comment: Formerly entitled: "A stratification of some moduli spaces of coherent systems on algebraic curves and their Hodge--Poincar\'e polynomials". The paper has been substantially shorten. Theorem 8.20 has been revised and corrected. Final version accepted for publication in International Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0407523 by other author

The Migdal Effect and Photon Bremsstrahlung in effective field theories of dark matter direct detection and coherent elastic neutrino-nucleus scattering

Dark matter direct detection experiments have limited sensitivity to light dark matter (below a few GeV), due to the challenges of lowering energy thresholds for the detection of nuclear recoil to below $\mathcal{O}(\mathrm{keV})$. While impressive progress has been made on this front, light dark matter remains the least constrained region of dark-matter parameter space. It has been shown that both ionization and excitation due to the Migdal effect and coherently-emitted photon bremsstrahlung from the recoiling atom can provide observable channels for light dark matter that would otherwise have been missed owing to the resulting nuclear recoil falling below the detector threshold. In this paper we extend previous work by calculating the Migdal effect and photon bremmstrahlung rates for a general set of interaction types, including those that are momentum-independent or -dependent, spin-independent or -dependent, as well as examining the rates for a variety of target materials, allowing us to place new experimental limits on some of these interaction types. Additionally, we include a calculation of these effects induced by the coherent scattering on nuclei of solar or atmospheric neutrinos. We demonstrate that the Migdal effect dominates over the bremsstrahlung effect for all targets considered for interactions induced by either dark matter or neutrinos. This reduces photon bremsstrahlung to irrelevancy for future direct detection experiments.Comment: 17 pages, 6 figure

Stability of Affine G-varieties and Irreducibility in Reductive Groups

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is identical with version 2 (version 3 is empty

Australian critical care nursing professionals' attitudes towards the use of traditional “chest physiotherapy” techniques

Background: Chest physiotherapy techniques, such as percussion, postural drainage, and expiratory vibrations, may be employed in a critical care setting. Physiotherapists are primarily responsible for their provision; however, nurses have also traditionally implemented these treatments. It is unclear whether nurses consider chest physiotherapy to be a part of their role, or how they perceive their knowledge and confidence pertaining to these techniques. Objective: To investigate the attitudes of nurses towards traditional chest physiotherapy techniques. Method: A total of 1222 members of the Australian College of Critical Care Nurses were invited to participate in an anonymous online survey. Results: There were 142 respondents (12%) with the majority (n = 132, 93%) having performed chest physiotherapy techniques in clinical practice. Most of them considered that the provision of chest physiotherapy was a part of nurse's role. Commonly cited factors influencing nurses' use of chest physiotherapy techniques were the availability of physiotherapy services, adequacy of nursing staff training and skill, and perceptions of professional roles. Conclusions: Nurses working in critical care commonly utilised traditional chest physiotherapy techniques. Further research is required to investigate the reasons why nursing professionals might assume responsibility for the provision of chest physiotherapy techniques, and if their application of these techniques is consistent with evidence-based recommendations

Structural basis for substrate specificity and regulation of nucleotide sugar transporters in the lipid bilayer

Nucleotide sugars are the activated form of monosaccharides used by glycosyltransferases during glycosylation. In eukaryotes the SLC35 family of solute carriers are responsible for their selective uptake into the Endoplasmic Reticulum or Golgi apparatus. The structure of the yeast GDP-mannose transporter, Vrg4, revealed a requirement for short chain lipids and a marked difference in transport rate between the nucleotide sugar and nucleoside monophosphate, suggesting a complex network of regulatory elements control transport into these organelles. Here we report the crystal structure of the GMP bound complex of Vrg4, revealing the molecular basis for GMP recognition and transport. Molecular dynamics, combined with biochemical analysis, reveal a lipid mediated dimer interface and mechanism for coordinating structural rearrangements during transport. Together these results provide further insight into how SLC35 family transporters function within the secretory pathway and sheds light onto the role that membrane lipids play in regulating transport across the membrane

Singular projective varieties and quantization

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This allows for generalization to the case of singular varieties. The set-up is explained in the first part of the contribution. The second part of the contribution is of tutorial nature. Necessary notions, concepts, and results of algebraic geometry appearing in this approach to quantization are explained. In particular, the notions of projective varieties, embeddings, singularities, and quotients appearing in geometric invariant theory are recalled.Comment: 21 pages, 3 figure

Double marking revisited

In 2002, the Qualifications and Curriculum Authority (QCA) published the report of an independent panel of experts into maintaining standards at Advanced Level (A-Level). One of its recommendations was for: ‘limited experimental double marking of scripts in subjects such as English to determine whether the strategy would signi-ficantly reduce errors of measurement’ (p. 24). This recommendation provided the impetus for this paper which reviews the all but forgotten literature on double marking and considers its relevance now

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe